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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 59150.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.bp1 | 59150bd4 | \([1, -1, 1, -1130980, -462640603]\) | \(2121328796049/120050\) | \(9054037819531250\) | \([2]\) | \(737280\) | \(2.1262\) | |
| 59150.bp2 | 59150bd3 | \([1, -1, 1, -370480, 81201397]\) | \(74565301329/5468750\) | \(412447058105468750\) | \([2]\) | \(737280\) | \(2.1262\) | |
| 59150.bp3 | 59150bd2 | \([1, -1, 1, -74730, -6340603]\) | \(611960049/122500\) | \(9238814101562500\) | \([2, 2]\) | \(368640\) | \(1.7796\) | |
| 59150.bp4 | 59150bd1 | \([1, -1, 1, 9770, -594603]\) | \(1367631/2800\) | \(-211172893750000\) | \([2]\) | \(184320\) | \(1.4330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59150.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 59150.bp do not have complex multiplication.Modular form 59150.2.a.bp
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
